We had a kit for a Da Vinci catapult which the girls put together.
I was very impressed by the range (by adjusting the tension it shot over 4 meters) but my favourite aspect was the secret math activity - changing the shape of your projectile (flat, round, spear etc), calculating the average distance over 5 shots, graphing the results then trying to discover why the shape effected the distance.
We had so much fun with the catapult that we decided to make a cannon as well. After discussing gunpowder and realising that it wasn't something we could use, we settled on an alternative - vinegar and bicarb.
We built the cannon out of an old bottle, a cork, cardboard wheels and a drinking straw base (after our first attempt backfired - the cannon literally flew backwards - the girls added some blue tack wedges under the wheels). This is a front loading cannon, so after loading the cannon with vinegar we would drop a shot of bicarb in (the 'shot' was a tablespoon of bicarb wrapped in a single ply piece of tissue), screw on the lid stuffed with the cork, aim and wait.